Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<cstdio>

using namespace std ;

int main()
{
	int n ,p ,miny = 1000000 ;
	double an ,s ,num[ 1000 ] ;
	cin >> n ;
	for( int i = 0 ; i < n ; i++ )
		cin >> num[ i ] ;

	sort( num ,num + n ) ;

	an = ( num[ n - 1 ] + num[ n - 2 ] ) / ( num[ 1 ] - num[ 0 ] ) ;
	for( int i = n - 1 ; i > 0 ; i-- )
	{
		if( num[ i ] - num[ i - 1 ] <= miny )
		{
			miny = num[ i ] - num[ i - 1 ] ;
			p = i ;
		}
	}
	if( p == n - 1 )
		s = ( num[ n - 3 ] + num[ n - 4 ] ) / ( num[ p ] - num[ p - 1 ] ) ;
	else
		s = ( num[ n - 1 ] + num[ n - 2 ] ) / ( num[ p ] - num[ p - 1 ] ) ;
	printf( "%.6f\n" ,max( an ,s ) ) ;
	return 0 ;
}